The Floyd-Warshall algorithm can solve the all-pairs shortest-paths problem on a directed graph $G = (V, E)$. Let $d_{ij}^{(k)}$ be the weight of a shortest path from vertex $i$ to vertex $j$ for which all intermediate vertices are in the set $\{1, 2, \ldots, k\}$ and $D^{(k)} = \left(d_{ij}^{(k)}\right)$ be a $n \times n$ matrix. Floyd-Warshall algorithm computes $D^{(k)}$ from $D^{(k-1)}$ as the following formula.

$d_{ij}^{(k)} =$ ______

Please complete the above formula.